Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations

Christian G. Claudel; Alexandre M. Bayen

doi:10.1109/acc.2010.5530615

Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations

Christian G. Claudel, Alexandre M. Bayen

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This article proposes a new method for data assimilation and data reconciliation applicable to systems modeled by conservation laws. The state of the system is written in the form of a scalar Hamilton-Jacobi (HJ) partial differential equation (PDE), for which the solution is fully characterized by a Lax-Hopf formula. Using the properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the constraints of the model are in standard convex form, and can be computed explicitly. This property enables us to identify a class of data assimilation and data reconciliation problems that can be formulated using convex programs in standard form.

Original language	English (US)
Title of host publication	Proceedings of the 2010 American Control Conference, ACC 2010
Publisher	IEEE Computer Society
Pages	4115-4120
Number of pages	6
ISBN (Print)	9781424474264
DOIs	https://doi.org/10.1109/acc.2010.5530615
State	Published - 2010

Publication series

Name	Proceedings of the 2010 American Control Conference, ACC 2010

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1109/acc.2010.5530615

Cite this

Claudel, C. G., & Bayen, A. M. (2010). Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 4115-4120). Article 5530615 (Proceedings of the 2010 American Control Conference, ACC 2010). IEEE Computer Society. https://doi.org/10.1109/acc.2010.5530615

@inproceedings{591996d780284d8488c46ca9c8fddd56,

title = "Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations",

abstract = "This article proposes a new method for data assimilation and data reconciliation applicable to systems modeled by conservation laws. The state of the system is written in the form of a scalar Hamilton-Jacobi (HJ) partial differential equation (PDE), for which the solution is fully characterized by a Lax-Hopf formula. Using the properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the constraints of the model are in standard convex form, and can be computed explicitly. This property enables us to identify a class of data assimilation and data reconciliation problems that can be formulated using convex programs in standard form.",

author = "Claudel, {Christian G.} and Bayen, {Alexandre M.}",

year = "2010",

doi = "10.1109/acc.2010.5530615",

language = "English (US)",

isbn = "9781424474264",

series = "Proceedings of the 2010 American Control Conference, ACC 2010",

publisher = "IEEE Computer Society",

pages = "4115--4120",

booktitle = "Proceedings of the 2010 American Control Conference, ACC 2010",

address = "United States",

}

Claudel, CG & Bayen, AM 2010, Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations. in Proceedings of the 2010 American Control Conference, ACC 2010., 5530615, Proceedings of the 2010 American Control Conference, ACC 2010, IEEE Computer Society, pp. 4115-4120. https://doi.org/10.1109/acc.2010.5530615

Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations. / Claudel, Christian G.; Bayen, Alexandre M.
Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society, 2010. p. 4115-4120 5530615 (Proceedings of the 2010 American Control Conference, ACC 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations

AU - Claudel, Christian G.

AU - Bayen, Alexandre M.

PY - 2010

Y1 - 2010

N2 - This article proposes a new method for data assimilation and data reconciliation applicable to systems modeled by conservation laws. The state of the system is written in the form of a scalar Hamilton-Jacobi (HJ) partial differential equation (PDE), for which the solution is fully characterized by a Lax-Hopf formula. Using the properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the constraints of the model are in standard convex form, and can be computed explicitly. This property enables us to identify a class of data assimilation and data reconciliation problems that can be formulated using convex programs in standard form.

AB - This article proposes a new method for data assimilation and data reconciliation applicable to systems modeled by conservation laws. The state of the system is written in the form of a scalar Hamilton-Jacobi (HJ) partial differential equation (PDE), for which the solution is fully characterized by a Lax-Hopf formula. Using the properties of the solution, we prove that when the data of the problem is prescribed in piecewise affine form, the constraints of the model are in standard convex form, and can be computed explicitly. This property enables us to identify a class of data assimilation and data reconciliation problems that can be formulated using convex programs in standard form.

UR - http://www.scopus.com/inward/record.url?scp=77957800863&partnerID=8YFLogxK

U2 - 10.1109/acc.2010.5530615

DO - 10.1109/acc.2010.5530615

M3 - Conference contribution

AN - SCOPUS:77957800863

SN - 9781424474264

T3 - Proceedings of the 2010 American Control Conference, ACC 2010

SP - 4115

EP - 4120

BT - Proceedings of the 2010 American Control Conference, ACC 2010

PB - IEEE Computer Society

ER -

Claudel CG, Bayen AM. Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations. In Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society. 2010. p. 4115-4120. 5530615. (Proceedings of the 2010 American Control Conference, ACC 2010). doi: 10.1109/acc.2010.5530615

Linear and quadratic programming formulations of data assimilation or data reconciliation problems for a class of Hamilton-Jacobi equations

Abstract

Publication series

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this